Thread: Power Series and radius/interval of convergence

Hi

The problem is to find the radius and interval of convergence of the series...

((-1)^(k+1)*(x+1)^k)/k from k=1 to infinity.

I have attempted using the ratio test for absolute convergence and have simplified it down to

rho=lim(k->infinity) |(x+1)|
I know it will converge absolutely if rho is less than 1 so i got |(x+1)|<1

So is the radius of convergence is 1 and the interval of convergence -2<x<0?

Originally Posted by Sam1111

Hi

The problem is to find the radius and interval of convergence of the series...

((-1)^(k+1)*(x+1)^k)/k from k=1 to infinity.

I have attempted using the ratio test for absolute convergence and have simplified it down to

rho=lim(k->infinity) |(x+1)|
I know it will converge absolutely if rho is less than 1 so i got |(x+1)|<1

So is the radius of convergence is 1 and the interval of convergence -2<x<0?

Almost: the interval of convergence contains both 0 and -2.

Tonio

Ok thanks! I was just making sure I was on the right track before checking the end points

Originally Posted by tonio

Almost: the interval of convergence contains both 0 and -2.

Tonio

That's not correct. If x= -2, the series is which does not converge. The series converges for .